Distance between 2 atoms in a crystal

  • Thread starter Nemo's
  • Start date
  • #1
69
0

Homework Statement



Given a crystal (cube) with regularly arranged atoms (Total 27 atoms)
The mass of each atom is 3.5*10^-25. The density of the crystal is 9.2*10^3
What is the shortest distance between the centres of two adjacent atoms?

Homework Equations



density = mass / volume

The Attempt at a Solution



Volume= (27*3.5*10^-25)/(9.2*10^3)=1.03*10^-27
Length(L)=1*10-9
Distance between two atoms is L/2=5.04*10^-10
Correct answer is 3.4*10^-9
 

Answers and Replies

  • #2
764
41
do you thinkthis is the correct answer?
 
  • #3
764
41
I think your "correct answer" is off by 10
 
  • #4
764
41
L is correct. Should you really be dividing by 2?
 
  • #5
69
0
Sorry the correct answer should be 3.4*10^-10
Should I divide by 3 then ? Why ?
 
  • #6
764
41
What you probably did was to assume the volume of 27 atoms had an atom at every corner and one between. But if you put this volume next to another, the atoms on the edges would be to close. In fact, the distance should be 3.
 
  • #7
69
0
But if you put this volume next to another, the atoms on the edges would be to close.
So the atoms on the edges would be closer than others and that's the required "shortest distance"?
I just can't really imagine what it looks like
 
  • #8
764
41
Maybe I wasn't clear. Put the atoms in a uniform rectangular three dimensional grid. My attachment shows the top view. Notice the volume is (3d)^3
 

Attachments

  • x120.jpg
    x120.jpg
    36.7 KB · Views: 873
  • #9
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
36,935
7,195
The difficulty is, what does volume (and therefore density) mean when applied to a crystal consisting of only 27 atoms? It does not say that the density given is for arbitrarily large chunks of this material - it is for specifically this crystal of 27 atoms. So I tend to agree with Nemo's answer.
 
  • #10
764
41
Good point, I guess whoever stated the "correct answer" thought it was for a large chunk.
 

Related Threads on Distance between 2 atoms in a crystal

Replies
2
Views
15K
  • Last Post
Replies
5
Views
10K
Replies
0
Views
16K
Replies
3
Views
7K
  • Last Post
Replies
3
Views
6K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
10
Views
2K
Replies
2
Views
4K
Replies
1
Views
690
  • Last Post
Replies
21
Views
408
Top